# I Description of Adiabatic Expansion

#### I_laff

I've seen the derivation for the adiabatic expansion of an ideal gas which gives the result $TV^{\gamma - 1} = constant$ which I understand. I have also seen the a similar result, $pV^{\gamma} = constant$. But I can't see how to get from the first expression to the second. Any ideas?

Related General Physics News on Phys.org

#### hilbert2

Gold Member
If you put $\frac{PV}{nR}$ in place of $T$ in the first equation, doesn't it become the second one, assuming that the number of moles $n$ remains constant in the expansion?

#### I_laff

From doing that you get $pV^{\gamma} = R(constant)$. So you just define a new constant on the RHS that contains $R$?

#### sophiecentaur

Gold Member
Isn't this a straightforward bit of Text Book derivation? Do you not have access to one?

#### hilbert2

Gold Member
Yes, it's a different constant then, the original one multiplied by $nR$.

#### sophiecentaur

Gold Member
If you don't have a text book, try the Hyperphysics website. They have a fair amount of stuff on the gas laws.

#### I_laff

Isn't this a straightforward bit of Text Book derivation? Do you not have access to one?
You are probably right, however I don't have a textbook on thermodynamics. I thought of substituting $\frac{pV}{nR}$ but didn't see how to remove $nR$ from the final expression. Since they're constant, I guess it's obvious the new constant contains these terms.

#### I_laff

If you don't have a text book, try the Hyperphysics website. They have a fair amount of stuff on the gas laws.
Thanks, I'll check it out .

#### sophiecentaur

Gold Member
Thanks, I'll check it out .
There are other on-line sources which are an alternative to a text book but Hyperphysics is fairly user friendly.

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving